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This thesis focuses on data structures and algorithms used in motion detection and imaging in complex settings. The work consists of four projects, addressing different aspects of imaging with a synthetic aperture radar (SAR) system or in an inverse synthetic aperture radar (iSAR) setting. In the first project, I analyzed an algorithm for the detection of moving targets in SAR using robust principal component analysis (RPCA). In the second project, I introduced an extension of the SAR data structure to tensors and a modified tensor RPCA algorithm, to improve detection of slowly moving targets. In the third project, I introduced a cross correlation data structure for iSAR imaging of low earth orbit (LEO) fast moving satellites, as well as novel imaging algorithms adapted to the cross correlation data structure. In the fourth project, I extended the problem to rotating satellites, analyzed the effect rotation has on performance, and showed how the rotation parameters can be extracted from the data. In a broad sense, all of these projects explore the effect data representation can have in imaging algorithms. The RPCA problems show that specific features in the raw data can be be exploited to detect motion. Moreover, the specific model of the data and different ways in which they are represented can significantly improve the performance of linear algebra and optimization based tools when applied to this problem. In the correlation based imaging problems, the choice of an appropriate data representation can provide insight into both improved imaging algorithms and their analysis. While these projects are distinct, they all demonstrate the importance of the choice of data structures and representations in imaging problems. The specific data structure may not only improve the applicability of previously used algorithms, but can also provide insight into extensions and modifications, as well as a rigorous mathematical analysis of the imaging algorithms.

In many networked decision-making settings, information about the world is distributed across multiple agents and agents’ success depends on their ability to aggregate and reason about their local information over time. This paper presents a computational model of information aggregation in such settings in which agents’ utilities depend on an unknown event. Agents initially receive a noisy signal about the event and take actions repeatedly while observing the actions of their neighbors in the network at each round. Such settings characterize many distributed systems such as sensor networks for intrusion detection and routing systems for Internet traffic. Using the model, we show that (1) agents converge in action and in knowledge for a general class of decision-making rules and for all network structures; (2) all networks converge to playing the same action regardless of the network structure; and (3) for particular network configurations, agents can converge to the correct action when using a well-defined class of myopic decision rules. These theoretical results are also supported by a new simulation-based open-source empirical test-bed for facilitating the study of information aggregation in general networks.

We consider imaging of fast moving small objects in space, such as low earth orbit satellites, which are also rotating around a fixed axis. The imaging system consists of ground based, asynchronous sources of radiation and several passive receivers above the dense atmosphere. We use the cross-correlation of the received signals to reduce distortions from ambient medium fluctuations. Imaging with correlations also has the advantage of not requiring any knowledge about the probing pulse and depends weakly on the emitter positions. We account for the target's orbital velocity by introducing the necessary Doppler compensation. To image a fast rotating object we also need to compensate for the rotation. We show that the rotation parameters can be extracted directly from the auto-correlation of the data before the formation of the image. We then investigate and analyze an imaging method that relies on backpropagating the cross-correlation data structure to two points rather than one, thus forming an interference matrix. The proposed imaging method consists of estimating the reflectivity as the top eigenvector of the migrated cross-correlation data interference matrix. We call this the rank-1 image and show that it provides superior image resolution compared to the usual single-point migration scheme for fast moving and rotating objects. Moreover, we observe a significant improvement in resolution due to the rotation leading to a diffraction limited resolution. We carry out a theoretical analysis that illustrates the role of the two point migration method as well as that of the inverse aperture and rotation in improving resolution. Extensive numerical simulations support the theoretical results.

We develop an imaging algorithm that exploits strong scattering to achieve super-resolution in changing random media. The method processes large and diverse array datasets using sparse dictionary learning, clustering, and multidimensional scaling. Starting from random initializations, the algorithm reliably extracts the unknown medium properties necessary for accurate imaging using back-propagation, \\(_2\\) or \\(_1\\) methods. Remarkably, scattering enhances resolution beyond homogeneous medium limits. When abundant data are available, the algorithm allows the realization of super-resolution in imaging.

We develop an imaging algorithm that exploits strong scattering to achieve super-resolution in changing random media. The method processes large and diverse array datasets using sparse dictionary learning, clustering, and multidimensional scaling. Starting from random initializations, the algorithm reliably extracts the unknown medium properties necessary for accurate imaging using back-propagation, \\(\\ell_2\\) or \\(\\ell_1\\) methods. Remarkably, scattering enhances resolution beyond homogeneous medium limits. When abundant data are available, the algorithm allows the realization of super-resolution in imaging.

We present a novel approach for extracting 3D atomic-level information from transmission electron microscopy (TEM) images affected by significant noise. The approach is based on formulating depth estimation as a semantic segmentation problem. We address the resulting segmentation problem by training a deep convolutional neural network to generate pixel-wise depth segmentation maps using simulated data corrupted by synthetic noise. The proposed method was applied to estimate the depth of atomic columns in CeO2 nanoparticles from simulated images and real-world TEM data. Our experiments show that the resulting depth estimates are accurate, calibrated and robust to noise.

We present a novel approach for extracting 3D atomic-level information from transmission electron microscopy (TEM) images affected by significant noise. The approach is based on formulating depth estimation as a semantic segmentation problem. We address the resulting segmentation problem by training a deep convolutional neural network to generate pixel-wise depth segmentation maps using simulated data corrupted by synthetic noise. The proposed method was applied to estimate the depth of atomic columns in CeO2 nanoparticles from simulated images and real-world TEM data. Our experiments show that the resulting depth estimates are accurate, calibrated and robust to noise.

We propose a methodology that exploits large and diverse data sets to accurately estimate the ambient medium's Green's functions in strongly scattering media. Given these estimates, obtained with and without the use of neural networks, excellent imaging results are achieved, with a resolution that is better than that of a homogeneous medium. This phenomenon, also known as super-resolution, occurs because the ambient scattering medium effectively enhances the physical imaging aperture. This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible.

Due to computational constraints, climate simulations cannot resolve a range of small-scale physical processes, which have a significant impact on the large-scale evolution of the climate system. Parameterization is an approach to capture the effect of these processes, without resolving them explicitly. In recent years, data-driven parameterizations based on convolutional neural networks have obtained promising results. In this work, we provide an in-depth analysis of these parameterizations developed using data from ocean simulations. The parametrizations account for the effect of mesoscale eddies toward improving simulations of momentum, heat, and mass exchange in the ocean. Our results provide several insights into the properties of data-driven parameterizations based on neural networks. First, their performance can be substantially improved by increasing the geographic extent of the training data. Second, they learn nonlinear structure, since they are able to outperform a linear baseline. Third, they generalize robustly across different CO2 forcings, but not necessarily across different ocean depths. Fourth, they exploit a relatively small region of their input to generate their output. Our results will guide the further development of ocean mesoscale eddy parameterizations, and multiscale modeling more generally.